"Dreadful news from London. My thoughts are with all those affected," Sturgeon posted on her official Twitter page.
Earlier on Saturday, local media reported that a van had hit several pedestrians on London Bridge while a stabbing attack took place at the Borough Market.
London Metropolitan Police confirmed they were dealing with an incident on London Bridge, Borough Market and Vauxhall area. They later declared that the incident at Vauxhall was not connected to the other two incidents.
UK Prime Minister Theresa May said that the incident was being treated as a potential act of terrorism.
Early on Sunday, police declared the London Bridge and Borough Market incidents as terrorist incidents.